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Thread: Why do root movements a fourth away tend to weaken the tonality of the key?

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    Default Why do root movements a fourth away tend to weaken the tonality of the key?

    Root movements a fifth away tend to strengthen the tonality of the key, while root movements a fourth away tend to weaken the tonality of the key.
    This is because we tend to hear a fifth as "root on bottom," and we tend to hear fourths as "root on top." This is due to the harmonic series.
    Schoenberg explores this in his book Structural Functions of Harmony.

    Also, the structure of the harmonically imperfect C major diatonic scale adds to this weakening; the semitone E-F acts as a leading tone to reinforce F, not G or C; b-C reinforces C; but there is no leading tone to reinforce G.

    So the "triumvirate" of IV-I-V is formed, as a section of the circle of fifths/fourths:

    IV.......I......V

    F.........C.....G

    The C major scale is thus designed for travel, not harmonic stability. This is what I mean by "imperfect harmonically." In a sense, it's not really "imperfect" or flawed; it just is what it is, and does what it does.
    Last edited by millionrainbows; Jul-18-2019 at 14:17.

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    Senior Member EdwardBast's Avatar
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    It would help if you could clarify what you mean by root movements a fifth away versus root movements a fourth away.

    Here are two diatonic circles of triads in C major. Which are you calling motion by 5ths and which motions by 4ths:

    1. C - F - B° - Em - Am - Dm - G - C

    2. C - G - Dm - Am - Em - B° - F - C

    I don't care from a terminological perspective which way you name them, I'm only interested in knowing what motion you are saying is tonality weakening.

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    Quote Originally Posted by EdwardBast View Post
    It would help if you could clarify what you mean by root movements a fifth away versus root movements a fourth away.

    Here are two diatonic circles of triads in C major. Which are you calling motion by 5ths and which motions by 4ths:

    1. C - F - B° - Em - Am - Dm - G - C

    2. C - G - Dm - Am - Em - B° - F - C

    I don't care from a terminological perspective which way you name them, I'm only interested in knowing what motion you are saying is tonality weakening.
    No, what motion combined with what interval.

    Apparently, from your question and the way you've posed it, you haven't quite 'grokked' the meaning of directionality in the circular, recursive scheme of tonality. This is what I keep saying is 'pitch identity' rather than 'pitch quantity.'

    C up to F = C down to F, etc. Both reinforce F as a new tonic, because we hear fourths as root on top, and fifth as root on bottom. This is a strong or ascending progression, since the destination root F has 'usurped' the power of the starting point C.

    Root movement a fourth up (C-F) is equal to a fifth down (C-F); root movement a fifth down is equal to a fourth up.

    "Directionality" is thus movement in time which works in either direction; what are we "going to" and where are we "coming from." Where are we "ending up?"

    Remember how you dismissed 'directionality' in the interval size thread? Well, don't dismiss it here.

    Schoenberg Roots 1 200 dpi .jpg Schoenberg Roots 2 200 dpi .jpg
    Last edited by millionrainbows; Jul-20-2019 at 12:17.

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    Senior Member EdwardBast's Avatar
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    So you mean the direction of the first progression I wrote. I'm not dismissing directionality, just asking you which direction. Your circumlocution brings to mind a bit of old wisdom: "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    Systematically exploiting motion in that direction is the way tonality was established. Your argument is absurd.
    Last edited by EdwardBast; Jul-20-2019 at 14:30.

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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by millionrainbows View Post
    Root movements a fifth away tend to strengthen the tonality of the key, while root movements a fourth away tend to weaken the tonality of the key.
    This is because we tend to hear a fifth as "root on bottom," and we tend to hear fourths as "root on top." This is due to the harmonic series.
    Schoenberg explores this in his book Structural Functions of Harmony.
    I don't understand this. Either you're not explaining what you mean clearly, or what you're trying to say doesn't make sense.

    If we establish the tonality of C major, and then strike a C major chord with C as root, how does moving next to an F chord (root F, up or down from C) or a G chord (root G, up or down from C) either weaken or strengthen the tonality we've established? Dominant and subdominant relationships are both components of the system of relationships which constitute the tonality. What is it that's weakened or strengthened by the use of them? Or are you talking about something else?

    Let me fish around a bit...

    If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced G chord, we will perceive that we've moved from the tonic to the dominant in the tonality of C regardless of whether we've moved the root by a fourth downward or a fifth upward from C.

    If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced F chord in root position, moving the root either a fourth up or a fifth down from C, we may perceive that we've moved from the dominant to the tonic in the tonality of F.

    The difference in our perceptions in these two cases is presumably rooted in our expectations of how tonic, dominant and subdominant function in the tonal system we normally employ. If this is part of what you're saying, I understand it. But I don't see what difference it makes whether we've moved the root by a fourth or a fifth, or how doing either one strengthens or weakens the sense of tonality. It seems to me that in doing either we're establishing and defining a tonality by means of its essential components.
    Last edited by Woodduck; Jul-21-2019 at 03:09.

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    I'm surprised at your reactions, especially since this is a very logical concept by Schoenberg, with excerpts from the book. It's all been explained clearly by me.
    Unless there's a pedantic glitch, I too am mystified by your miscomprehension.

    If it's not me, it must be Schoenberg. I'm just the messenger.
    Last edited by millionrainbows; Jul-21-2019 at 16:38.

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    Quote Originally Posted by Woodduck View Post
    If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced G chord, we will perceive that we've moved from the tonic to the dominant in the tonality of C regardless of whether we've moved the root by a fourth downward or a fifth upward from C.


    True. The two are equivalent.

    If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced F chord in root position, moving the root either a fourth up or a fifth down from C, we may perceive that we've moved from the dominant to the tonic in the tonality of F.
    True.

    The difference in our perceptions in these two cases is presumably rooted in our expectations of how tonic, dominant and subdominant function in the tonal system we normally employ. If this is part of what you're saying, I understand it.
    That's part of it.

    But I don't see what difference it makes whether we've moved the root by a fourth or a fifth, or how doing either one strengthens or weakens the sense of tonality. It seems to me that in doing either we're establishing and defining a tonality by means of its essential components.
    That part of your statement doesn't make sense. There is a difference in moving the root by a fourth, depending on which direction.

    Going up a fourth, C-F, establishes F. (fourths are heard as root on top).
    The root note of the first chord is degraded, becoming only the fifth of the second chord.

    Going down a fourth is C-G, establishing C. This is equivalent to a fifth up, C-G, in which we hear fifths as root on bottom.
    The fifth of the first chord always advances to become the root of the second chord.

    (this is explained in the footnote of the book excerpt).

    You guys are having a pedantic mind-glitch, I guess.

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    A similar concept is touched on in Rosen's book The Classical Style, he shows a diagram of the circle of 5ths (but not as a circle as two lines diverging away from each other) and suggests that the side going up in 5ths is more harmonically stable than the side going back in 4ths. He also states that the major scale is more harmonically stable than the minor scale, this is why Classical era composers chose to compose in major keys more often than minor.
    Last edited by tdc; Jul-21-2019 at 20:35.

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    Quote Originally Posted by tdc View Post
    A similar concept is touched on in Rosen's book The Classical Style, he shows a diagram of the circle of 5ths (but not as a circle as two lines diverging away from each other) and suggests that the side going up in 5ths is more harmonically stable than the side going back in 4ths. He also states that the major scale is more harmonically stable than the minor scale, this is why Classical era composers chose to compose in major keys more often than minor.
    Yes, as long as you understand that fifths are stable with root on bottom (harmonically/vertically) or with root as first root note (horizontally).

    This insight is a luxury of already "grokking" this concept, and may confuse things.

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    Quote Originally Posted by millionrainbows View Post
    Yes, as long as you understand that fifths are stable with root on bottom (harmonically/vertically) or with root as first root note (horizontally).

    This insight is a luxury of already "grokking" this concept, and may confuse things.
    It doesn't seem confusing as much as possibly an example of stating something in a way that makes things sound more complex than is necessary, although maybe I'm failing to grasp something. Simply put if you reverse the order of the root with the fifth, a fifth is no longer a fifth but a fourth, so your point seems self evident. Is there something more to this I'm failing to "grok"?
    Last edited by tdc; Jul-22-2019 at 00:50.

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    Quote Originally Posted by tdc View Post
    It doesn't seem confusing as much as possibly an example of stating something in a way that makes things sound more complex than is necessary, although maybe I'm failing to grasp something. Simply put if you reverse the order of the root with the fifth, a fifth is no longer a fifth but a fourth, so your point seems self evident. Is there something more to this I'm failing to "grok"?
    No, I'm just being cautious because of the presence of EdwardBast and Woodduck. You call it 'self evident,' they call it absurd and confusing.

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    Quote Originally Posted by millionrainbows View Post
    No, I'm just being cautious because of the presence of EdwardBast and Woodduck. You call it 'self evident,' they call it absurd and confusing.
    But what exactly is your question? The question in the title of the thread seems to be answered by both Schoenberg and Rosen. Schoenberg's language seems a bit more ornate* than Rosen's, and Rosen adds one significant point - helpful, at least, to my understanding: all harmonics rise from a note. Thus, if I understand him correctly, the dominant, as the third harmonic, is more closely associated with the tonic than the subdominant. But as Woodduck says, neither of them, on their own, indicate a change of an established tonic in the composition.

    As for your "harmonically imperfect C diatonic scale," are you saying there is something unique about C Major that distinguishes it from other major scales? (In the world of equal temperament.)

    *And I would be careful of descriptive terms - Schoenberg describes the dominant as an inferior tone, while Rosen describes it as powerful, even though they are making the same point.
    Last edited by jegreenwood; Jul-22-2019 at 17:05.

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    Quote Originally Posted by millionrainbows View Post
    No, I'm just being cautious because of the presence of EdwardBast and Woodduck. You call it 'self evident,' they call it absurd and confusing.
    Actually, EdwardBast and Woodduck call it absurd or confusing when it's absurd or confusing. We're pretty bright fellows who say things very precisely and appreciate the same in others. If we don't get what you're saying you might at least consider the possibility that you need to explain things better.
    Last edited by Woodduck; Jul-22-2019 at 17:21.

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    Quote Originally Posted by jegreenwood View Post
    But what exactly is your question? The question in the title of the thread seems to be answered by both Schoenberg and Rosen. Schoenberg's language seems a bit more ornate* than Rosen's, and Rosen adds one significant point - helpful, at least, to my understanding: all harmonics rise from a note. Thus, if I understand him correctly, the dominant, as the third harmonic, is more closely associated with the tonic than the subdominant. But as Woodduck says, neither of them, on their own, indicate a change of an established tonic in the composition.
    Well then, conversely, you seem to have come to the same conclusion as Woodduck and EdwardBast, that points to this thread being absurd and confusing. If that satisfies you, fine.

    I don't think Schoenberg's intent was to show how these root movements establish a large-scale tonal area, but rather to show tendencies in how they can weaken or strengthen tonal tendencies.

    As for your "harmonically imperfect C diatonic scale," are you saying there is something unique about C Major that distinguishes it from other major scales? (In the world of equal temperament.)
    No, I don't wish to point out the C major scale's uniqueness; it does what it does. Considering scales solely as vehicles for establishing tonality, there are other scales more suited for this, and the C major scale is not "perfect" in establishing tonality.

    The example I always use comes from jazz, in which scales are matched with chords in terms of their maximum harmonic compatibility.
    One tenet of jazz is: when playing over a C major seventh chord, DO NOT use the C major scale; use C lydian. Why? Because of the note "F".

    *And I would be careful of descriptive terms - Schoenberg describes the dominant as an inferior tone, while Rosen describes it as powerful, even though they are making the same point.
    I haven't read the Charles Rosen material, and I didn't bring him up, so you should be careful who you ascribe these ideas to. The ideas I have exposed here all came from Schoenberg.
    Last edited by millionrainbows; Jul-22-2019 at 17:41.

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    Quote Originally Posted by Woodduck View Post
    Actually, EdwardBast and Woodduck call it absurd or confusing when it's absurd or confusing. We're pretty bright fellows who say things very precisely and appreciate the same in others. If we don't get what you're saying you might at least consider the possibility that you need to explain things better.
    Do I have to explain Schoenberg's ideas about root movement in order for you to understand or accept them? Again, I don't think Schoenberg's intent was to show how these root movements establish a large-scale tonal area (if that's your point), but rather to show how they can weaken or strengthen tonal tendencies

    Your reply in post #5 already demonstrates that you seem to be missing a crucial point:

    But I don't see what difference it makes whether we've moved the root by a fourth or a fifth, or how doing either one strengthens or weakens the sense of tonality.
    But if you are talking about other factors in establishing large areas of tonality, then these "microcosms" of tonal tendencies do not concern you. If they don't interest you, fine.

    Frankly, I'm torn between wondering whether you & EdwardBast are sincerely confused, or whether you have some other reason for replying as you have.
    Last edited by millionrainbows; Jul-22-2019 at 17:55.

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